Optimal Regularity of Lower-Dimensional Obstacle Problems

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The Bernstein Technique for Integro-Differential Equations (2020, methodology): “Caffarelli, L., Silvestre, L.: The Evans–Krylov theorem for nonlocal fully nonlinear equations.”
Nonlinear Diffusion with Fractional Laplacian Operators (2012, background): “The linear or quasilinear elliptic theory has been actively studied recently in the works of Caffarelli and collaborators [6, 8, 24], Kassmann [44], Silvestre [60] and many others.”
Regularity of the obstacle problem for a fractional power of the laplace operator (2007, methodology): “In other words, u is semiconvex, and for each point x there is a paraboloid touching u from below: u(y) ≥ u(x) + B · (y − x) − C 2 |x − y|2 where B is any vector of the subdifferential of u(y) + (C/2)|x − y|2 at x .”
Nonlinear Porous Medium Flow with Fractional Potential Pressure (2010, methodology): “onic extension to the upper plane of the space with one more dimension and then taking the boundary normal derivative, and has been used in the study or variational problems with thin obstacles as in [3], see also [9, 10]. For s6= 1 /2 the method has been recently developed in [12], it involves elli”
Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, background): “On the other hand, it is mentioned in heat control problems by [10].”